Physical Principles of Electron Microscopy: An Introduction to TEM ...

116 Chapter 4
A simple example of phase contrast is the appearance, in a defocused
image, of a dark Fresnel fringe just inside a small hole in the specimen. The
separation of this fringe from the edge of the hole increases with the amount
of defocus. In fact, its separation from the edge will change if the objective
focusing power varies for electrons traveling along different azimuthal
directions relative to the optic axis, i.e,. if objective astigmatism is present.
Therefore, the Fresnel fringe inside a circular hole is sometimes used as a
guide to adjusting the objective-lens stigmator.
Phase contrast also occurs as a result of the regular spacing of atoms in a
crystal, particularly if the specimen is oriented so that columns of atoms are
parallel to the incident electron beam. The contrast observable in high
magnification (M > 500,000) images is of this type and allows the lattice of
atoms (projected onto a plane perpendicular to the incident direction) to be
seen directly in the image. The electron-wave explanation is that electrons
traveling down the center of an atomic column have their phase retarded
relative to those that travel in between the columns. However, the basic
effect can be understood by treating the electrons as particles, as follows.
In Fig. 4-17, we represent a crystalline specimen in the TEM by a single
layer of atoms (of equal spacing d ) irradiated by a parallel electron beam
with a uniform current density. The nuclei of the atoms elastically scatter the
electrons through angles that depend inversely on the impact parameter b of
each electron, as indicated by Eq. (4.11). If the objective lens is focused on
the atom plane and all electrons are collected to form the image, the uniform
illumination will ensure that the image contrast is zero. If now the objective
current is increased slightly (overfocus condition), the TEM will image a
plane below the specimen, where the electrons are more numerous at
positions vertically below the atom positions, causing the atoms to appear
bright in the final image. On the other hand, if the objective lens is
weakened in order to image a virtual-object plane just above the specimen,
the electrons appear to come from positions halfway between the atoms, as
shown by the dashed lines that represent extrapolations of the electron
trajectories. In this underfocus condition, the image will show atoms that
appear dark relative to their surroundings.
The optimum amount of defocus �z can be estimated by considering a
close collision with impact parameter b